Since the 16th century, the design of optical components has centered on homogenous dielectric media. Such optical components are limited by the achievable wave vectors and dispersion relations at optical frequencies in the medium. This is severely limiting since the refractive indices of typical dielectric materials are both modest and essentially constant below their optical gaps. This limitation has been overcome in the last decade through the development of photonic devices in heterogeneous materials including waveguides, resonators and photonic crystals.
Photonic crystals are artificially fabricated structures, typically made of a dielectric material, such as glass or silicon, and typically containing a periodic array of holes. Photonic crystals were first described by Yablonovitch in 1987 and were first constructed by mechanically drilling holes in ceramic blocks. The propagation of electromagnetic radiation, such as light, through such a heterogeneous periodic medium is quite complicated, especially when the wave-length becomes comparable to the periodicity of the structure. The propagation of the electromagnetic radiation can be described using a dispersion relation that relates the frequency to the wave-number. The dispersion relation depends on both the refractive index and also the geometry. The slope of the dispersion curve gives the group velocity, i.e., the effective velocity with which electromagnetic energy propagates in this medium. In photonic crystals the group velocity can become very small and even zero. Furthermore, a periodic array of materials with different indices of refraction gives rise to forbidden frequencies of light known as the optical or photonic band-gap (“PBG”). The photonic crystal acts as a reflector for light of those frequencies. Finally, by putting in defects wherein one deviates from periodicity in selected regions, one can build a number of interesting devices such as resonant cavities and lasers.
Photonic crystals are nanofabricated two- and three-dimensional periodic structures in glass and semiconductors that allow one to design or to engineer the dispersion relation of the medium. They can be designed with well-defined photonic bandgaps, which are frequency bands within which the propagation of electromagnetic waves is forbidden irrespective of the propagation direction in space and polarization of the incoming light. When combined with high index contrast slabs in which light can be efficiently guided, nanofabricated two-dimensional photonic bandgap mirrors can be fabricated to confine and concentrate light into extremely small volumes and to obtain very high field intensities that enable a variety of applications. Fabrication of optical structures has evolved to a precision that allows the control of light within etched nanostructures. As one example, nanofabricated high reflectivity mirrors can be used to define high-Q cavities in Vertical Cavity Surface Emitting Lasers (VCSELs). For example, room temperature lasing in the smallest optical cavities with mode volumes down to 2.5 (λ/2/nslab)3, or 0.03 μm3 in InGaAsP emitting at 1.55 μm have been demonstrated. As the mode volumes of nano-cavities are decreased, the coupling efficiency between the spontaneous emission within the cavity and the lasing mode can be significantly improved. Furthermore, sub-wavelength nano-optic cavities can be used for efficient and flexible control over both emission wavelength and frequency.
Photonic crystal waveguides play a crucial role in photonic crystal integrated circuits. These waveguides are responsible for transferring light throughout the integrated circuit as well as for the coupling of light into and out of the integrated circuit. At ˜1.5 μm wavelengths, it is possible to use silicon as a low-absorption waveguide material, and to leverage upon the extensive fabrication and wafer preparation experience of the microelectronics industry. In particular, semiconductor on insulator (SOI) structures lend themselves well to fabrication of single mode waveguides from high index silicon and the fabrication of passive two-dimensional (“2-D”) photonic crystal structures. When designed properly, a semiconductor on insulator layer can serve as a high index optical waveguide, and can be patterned to define 2-D PBG material.
Although photonic crystals and photonic devices are currently fabricated, they are static structures. They possess the dispersion relation and characteristics that exist when they are fabricated.
A variety of materials exhibit ferroelectricity including perovskites with the composition ABO3, where A and B are suitable metals. A few common examples are barium titanate (BaTiO3), lead titanate (PbTiO3) and lithium niobate (LiNbO3). Ferroelectric materials exhibit spontaneous polarization and form domain patterns that can be switched through applied fields, such as electrical, optical and mechanical fields. They possess high refractive index and birefringence that can be tuned through the application of electric fields. BaTiO3 is non-polar and cubic above its Curie temperature of 403 K, but is spontaneously electrically polarized along a <100> cubic direction and is spontaneously distorted into a tetragonal symmetry below the Curie temperature. The reduction in symmetry at its phase transition means that the ferroelectric can exist in six equivalent forms or variants below the Curie temperature. A typical crystal contains a mixture of variants with domains of one variant separated from the other by domain walls. The domain pattern can be changed by the application of electric field and stress as one variant switches to another. This material is a nonlinear anisotropic dielectric at room temperature.
Ferroelectric perovskites like barium titanate display the electro-optic effect wherein the refractive index can be changed through the application of electric field. This electrical-optical coupling has two sources. The first is the intrinsic electro-optic coupling (that with fixed domain pattern) under moderate fields, and the second is an extrinsic electro-optic coupling (that associated with changing domain patterns) under sufficiently high fields (above the coercive field). The latter is a consequence of the fact that ferroelectric perovskites are birefringent materials, in which the refractive index in the direction of the spontaneous polarization is different from the refractive index in a direction perpendicular to the spontaneous polarization. When the domains are switched through the application of electric field, the direction of spontaneous polarization and consequently the refractive index also changes.
Ferroelectric perovskites like barium titanate are also wide-band gap semiconductors and display the photorefractive effect that can be influenced by doping. When illuminated with light in the visible spectrum, charges are excited into the conduction band from traps in the crystal. These charges can diffuse away from the point of excitation before they are retrapped. When there is a gradient in the illumination pattern, this process can establish space charge fields with charges accumulating in the darker regions. The presence of the electric field modulates the index of refraction of the material which in turn modulates light incident on the crystal. This mechanism is known as electrical fixing, and can be used to permanently store holograms recorded via the photorefractive effect. The same internal fields can also be used to locally align the domains of the crystal. Typically, a strong external field is applied and the internal photorefractive field either adds or subtracts from it to cause the domains to flip.
High-quality bulk crystals of LiNbO3 can be synthesized. The modulation of the refractive index via the 3rd order nonlinear optical coefficient using DC electric fields has led to the development of commercial high speed (10-40 Gb/sec) electro-optic modulators formed as diffused waveguides in bulk LiNbO3. However, these modulators offer very limited tunability. These devices are limited in their capabilities and necessarily are fabricated at the millimeter scale or larger.
There is a need for apparatus that can manipulate light, that can be small enough to allow fabrication of the analog of integrated circuits, and that can operate in a tunable fashion.